IEICE TRANSACTIONS on Fundamentals
Adaptive AR Spectral Estimation Based on Wavelet Decomposition of the Linear Prediction Error
Summary :
A new adaptive AR spectral estimation method is proposed. While conventional least-squares methods use a single windowing function to analyze the linear prediction error, the proposed method uses a different window for each frequency band of the linear prediction error to define a cost function to be meinemized. With this approach, since time and frequency resolutions can be traded off throughout the frequency spectrum, an improvement on the precision of the estimates is achieved. In this paper, a wavelet-like time-frequency resolution grid is used so that low-frequency components of the linear prediction error are analyzed through long windows and high-frequency components are analyzed through short ones. To solve the optimization problem for the new cost function, special properties of the correlation matrix are used to derive an RLS algorithm on the order of M2, where M is the number of parameters of the AR model. Computer simulations comparing the performance of conventional RLS and the proposed methods are shown. In particular, it can be observed that the wavelet-based spectral estimation method gives fine frequency resolution at low frequencies and sharp time resolution at high frequencies, while with conventional methods it is possible to obtain only one of these characteristics.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.5 pp.665-673
- Publication Date
- 1996/05/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Digital Signal Processing
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Fernando Gil V. RESENDE Jr., Keiichi TOKUDA, Mineo KANEKO, "Adaptive AR Spectral Estimation Based on Wavelet Decomposition of the Linear Prediction Error" in IEICE TRANSACTIONS on Fundamentals,
vol. E79-A, no. 5, pp. 665-673, May 1996, doi: .
Abstract: A new adaptive AR spectral estimation method is proposed. While conventional least-squares methods use a single windowing function to analyze the linear prediction error, the proposed method uses a different window for each frequency band of the linear prediction error to define a cost function to be meinemized. With this approach, since time and frequency resolutions can be traded off throughout the frequency spectrum, an improvement on the precision of the estimates is achieved. In this paper, a wavelet-like time-frequency resolution grid is used so that low-frequency components of the linear prediction error are analyzed through long windows and high-frequency components are analyzed through short ones. To solve the optimization problem for the new cost function, special properties of the correlation matrix are used to derive an RLS algorithm on the order of M2, where M is the number of parameters of the AR model. Computer simulations comparing the performance of conventional RLS and the proposed methods are shown. In particular, it can be observed that the wavelet-based spectral estimation method gives fine frequency resolution at low frequencies and sharp time resolution at high frequencies, while with conventional methods it is possible to obtain only one of these characteristics.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e79-a_5_665/_p
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@ARTICLE{e79-a_5_665,
author={Fernando Gil V. RESENDE Jr., Keiichi TOKUDA, Mineo KANEKO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Adaptive AR Spectral Estimation Based on Wavelet Decomposition of the Linear Prediction Error},
year={1996},
volume={E79-A},
number={5},
pages={665-673},
abstract={A new adaptive AR spectral estimation method is proposed. While conventional least-squares methods use a single windowing function to analyze the linear prediction error, the proposed method uses a different window for each frequency band of the linear prediction error to define a cost function to be meinemized. With this approach, since time and frequency resolutions can be traded off throughout the frequency spectrum, an improvement on the precision of the estimates is achieved. In this paper, a wavelet-like time-frequency resolution grid is used so that low-frequency components of the linear prediction error are analyzed through long windows and high-frequency components are analyzed through short ones. To solve the optimization problem for the new cost function, special properties of the correlation matrix are used to derive an RLS algorithm on the order of M2, where M is the number of parameters of the AR model. Computer simulations comparing the performance of conventional RLS and the proposed methods are shown. In particular, it can be observed that the wavelet-based spectral estimation method gives fine frequency resolution at low frequencies and sharp time resolution at high frequencies, while with conventional methods it is possible to obtain only one of these characteristics.},
keywords={},
doi={},
ISSN={},
month={May},}
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TY - JOUR
TI - Adaptive AR Spectral Estimation Based on Wavelet Decomposition of the Linear Prediction Error
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 665
EP - 673
AU - Fernando Gil V. RESENDE Jr.
AU - Keiichi TOKUDA
AU - Mineo KANEKO
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 1996
AB - A new adaptive AR spectral estimation method is proposed. While conventional least-squares methods use a single windowing function to analyze the linear prediction error, the proposed method uses a different window for each frequency band of the linear prediction error to define a cost function to be meinemized. With this approach, since time and frequency resolutions can be traded off throughout the frequency spectrum, an improvement on the precision of the estimates is achieved. In this paper, a wavelet-like time-frequency resolution grid is used so that low-frequency components of the linear prediction error are analyzed through long windows and high-frequency components are analyzed through short ones. To solve the optimization problem for the new cost function, special properties of the correlation matrix are used to derive an RLS algorithm on the order of M2, where M is the number of parameters of the AR model. Computer simulations comparing the performance of conventional RLS and the proposed methods are shown. In particular, it can be observed that the wavelet-based spectral estimation method gives fine frequency resolution at low frequencies and sharp time resolution at high frequencies, while with conventional methods it is possible to obtain only one of these characteristics.
ER -
English
